It sounds like OP is just attracted to the degree for the name, and likes the idea of tacking on 'Princeton University' to his CV. Likely, OP has some interest in politics, and thinks that having a master's in public administration coupled with a JD will help further his career goals. Ironically, the reason degrees like the MPA at Princeton require work experience is to avoid students like this.
The dual JD/MPA program at Princeton is highly competitive. Not only because you need to get into each school individually (which, considering you're a freshman at UF, there's no way of knowing you will), but also because you need to have good reason for wanting to pursue both degrees. The reason that Princeton pays for your MPA and your JD is so that you can go into civil service with a low debt-load. But they're not going to hand you a scholarship without you having demonstrated some level of success and dedication to the field of civil service through work experience.
Loads of people are class presidents. Every school in America graduates a class president. But not every class president is going to put his or her neck on the line by serving in the Middle-East, or by working with USAID in Africa. There's a level of dedication that is a prerequisite to programs like this that, as a general rule, precludes those who are simply pursuing the program for self serving reasons.